Problem: Solve for $x$ : $x^2 + 6x - 27 = 0$
The coefficient on the $x$ term is $6$ and the constant term is $-27$ , so we need to find two numbers that add up to $6$ and multiply to $-27$ The two numbers $9$ and $-3$ satisfy both conditions: $ {9} + {-3} = {6} $ $ {9} \times {-3} = {-27} $ $(x + {9}) (x {-3}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 9) (x -3) = 0$ $x + 9 = 0$ or $x - 3 = 0$ Thus, $x = -9$ and $x = 3$ are the solutions.